Laser ultrasonic signal processing: A model-reference approach

Abstract

A model-reference approach is developed to solve the signal enhancement problem of a laser ultrasonics application for nondestructive evaluation. In this problem a sophisticated laser thermoelastic propagation model is used to synthesize the surface displacement of the specimen under test. Once synthesized, this model response is used as the reference signal in an optimal ͑minimum error variance͒ signal enhancement scheme. Both fixed and adaptive processors are considered in this application where it is shown that a significant improvement in signal levels can be achieved over the usual methods to enhance noisy data acquired from a Michelson interferometric measurement system and increase its overall sensitivity.

Numerical Calculation of the Spectrum of the Severe (1%) Lighting Current and Its First Derivative

“…sampling without an actual increase in frequency resolution; a longer record of non-zero samples of x[n] is required to truly increase the frequency resolution [5]. For a well-behaved x(t), if x(t) is also approximately time-and band-limited for the sampling defined in Eqn.…”

“…Interpolation to a finer frequency sampling can be achieved by appending zeros to x[n] to a length N zp [4,5]. The new frequency spacing is then ∆f zp = f s /N zp , and Eqns.…”

“…Let the FFT of the length N discrete-time signal x[n] be defined 2 as [4,5] 1 For numerical reasons we use an alternate but equivalent expression for the fraction in Eqn. 1:…”

“…4 is the definition of the Discrete Fourier Transform (DFT), and the FFT is a fast algorithm for computing the DFT [3,4,5]. We call Eqn.…”

“…Suppose we wish to compute the spectrum of a continuous-time signal x(t). One method for approximating the spectrum is as follows [4,5,6]. 3 First, we sample x(t) at f s samples per second to produce the length N array x[n]:…”